Question

The base of a cone and cylinder have the same radius 6cm, they have also the same height 8cm.The ratio of C.S.A of the cylinder to that of cone is​

Answer 1

Step-by-step explanation:

Ratio of curved surface area of cylinder and cone

= 2πrhπrh2+r2−−−−−√=2×6×86×62+82−−−−−√

= 966×10=9660=85 = 8 : 5

Answer 2

SOLUTION :-

Cylinder :-

Radius, r = 6 cm

Height, h = 8 cm

$\boxed{\bf C.S.A \ of \ cylinder = 2\pi r h }$

$\longrightarrow \sf 2\times \pi \times 6 \times 8 \\\\\longrightarrow 96 \pi$

Cone :-

Radius, r = 6 cm

Height, h = 8 cm

We know that,

$\bf l^2= h^2+r^2$

$\longrightarrow \sf l^2= 8^2+6^2\\\\\longrightarrow l^2= 64+36\\\\\longrightarrow l^2 = 100\\\\\longrightarrow l = 10$

Slant height, l = 10 cm

$\boxed{\bf C.S.A \ of \ cone = \pi rl }$

$\longrightarrow \sf \pi \times 6 \times 10 \\\\\longrightarrow 60 \pi$

Ratio of C.S.A of cylinder and cone = 96π : 60π

                                                           = 12 × 8 : 12 × 5

                                                           = 8 : 5